Expansion computed for the quadratic map for 1025 parameters using heuristic partitions based on the derivative of the map - Open Research Data - Bridge of Knowledge

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Expansion computed for the quadratic map for 1025 parameters using heuristic partitions based on the derivative of the map

Description

Expansion data computed for the quadratic map by the program that implements the algorithms introduced in the paper “Rigorous computation of expansion in one-dimensional dynamics” by Paweł Pilarczyk, Michał Palczewski and Stefano Luzzatto.

The computation was conducted for 1025 uniformly spaced parameter values in [1.4,2] using heristically defined partitions of 5000 intervals outside the critical neighborhood of radius δ=0.001. There are a few datasets in the package obtained for different scaling of the partition based on the derivative of the map. The numbers correspond to the following ideas (please, see the paper for in-depth explanation):
– run20d00.csv: the uniform partition (to be used for reference),
– run20d01.csv: linear dependence on the derivative,
– run20d02.csv: quadratic dependence on the derivative,
– run20d03.csv: cubic dependence on the derivative,
– run20d04.csv: exponential dependence on the derivative,
– run20d05.csv: double exponential dependence on the derivative,
– run20d09.csv: inverse-exponential dependence on the derivative (numbered −1 in the paper).

The data is in the CSV format, with the first row containing column labels. The contents of the columns is the following:

  • level — the level of subdivision of the parameter interval (e.g. 10 for 2^10=1024 subintervals)
  • num — the identifier of the data piece in the collection at the given subdivision; the identifiers begin with 0
  • parMin — the left endpoint of the parameter interval (minimal parameter value)
  • parMax — the right endpoint of the parameter interval (maximal parameter value)
  • k — the total number of intervals on which the graph representation of the map was built (the critical neighborhood is counted here, too)
  • delta — the radius δ of the critical neighborhood
  • lambda — the computed expansion exponent λ
  • logC — log C if the constant C was computed, otherwise 0
  • lambda0 — the constant λ₀ if it was computed, otherwise 0
  • period — the period of a periodic orbit found (0 if none)
  • lambdaMax — an upper bound on the expansion exponent of the periodic orbit found (0 if none)
  • distFrom0out — the minimum guaranteed distance of the periodic orbit from 0
  • distFrom0in — an upper bound on the distance from 0 during the closest approach to 0
  • compTime — the computation time measured in seconds

This research was supported by the National Science Centre, Poland, within the grant OPUS 2021/41/B/ST1/00405. Some computations were carried out at the Centre of Informatics Tricity Academic Supercomputer & Network.

Dataset file

run20d00-09.zip
160.7 kB, S3 ETag 257ba5075c4341751a7a093c03e98e93-1, downloads: 0
The file hash is calculated from the formula
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.

Example script for calculation:
https://github.com/antespi/s3md5
download file run20d00-09.zip

File details

License:
Creative Commons: 0 1.0 open in new tab
CC 0
Public Domain Dedication
Raw data:
Data contained in dataset was not processed.

Details

Year of publication:
2025
Verification date:
2025-05-28
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
DOI:
DOI ID 10.34808/tfcb-6w33 open in new tab
Funding:
Series:
Verified by:
Gdańsk University of Technology

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